Transfers, Age Profiles, and Economic Growth: Contributions of NTA

1. Transfers, Age Profiles, and Economic Growth: Contributions of NTA Ronald Lee, October 22, 2006 Tokyo

2. This is a workshop. In spirit of workshop, I will discuss some theoretical ideas that are not fully worked out and some empirical work in progress. • Gretchen Donehower and Avi Ebenstein carried out the empirical analyses I will be reporting in the second half of my talk.

3. Plan of talk • Population change, transfers and economic growth—theoretical perspectives. • Implementation and comparison of these theoretical approaches for Taiwan. • Historical US data on changing age profiles, and how these are related to growth.

4. Some of the topics that NTA estimates can be used to study • Issues of generational equity that arise when public sector transfer systems change. Ditto for private transfers systems—generational squeezes.. • Guidance in designing and reforming systems of social support. • Population change and economic growth (dividends and beyond). • Long run projections of government budgets (Tim has worked on this with you). • Estimation of fiscal externalities to the birth of a child, or the arrival of an immigrant, or the departure of an emigrant. • Mapping the systems through which income is reallocated within an economy, including nonmarket reallocations. Understanding the unusual features of a country’s systems. • How transfer systems in a country are changing over time and the implications of these changes. • Make it possible to take transfer behavior into account in studies of saving behavior. • Study social inequities in transfer systems, for example by level of education or by race/ethnicity (the Brazil project has a paper on this).

5. Outline of rest of talk • Demographic transition, intergenerational transfers, and economic growth: theoretical approaches. • Empirical/Simulation explorations of these theories. • The changing shape of the economic life cycle in the US: preliminary historical results.

6. I. Golden rule steady states without age structure • Consider standard Solow growth model on golden rule steady state growth path • Saving rate is chosen to maximize steady state consumption, c • This requires that all labor earnings Yl be consumed and all capital earnings, Yk, be saved. • Together with a production function and a rate of population growth, n, this determines the level of consumption per capita, c, and capital per worker, k. • We can find the effect of a change in the population growth rate, n, on the steady state consumption, c, by differentiating:

7. With more rapid population growth, more output must be saved to equip new workers, and the optimal levels of k, y, and c will all be a bit lower. “capital dilution”.

8. II. Golden rule steady states with age structure: basic ideas • Now let the population have a steady state age structure e-nxl(x), and let steady state consumption and earnings by age be c(x) and yl(x). • In golden rule, the rate of return on capital and the discount rate equal n, the pop gr rate. • Let C = the present value of life time consumption discounted at rate n and survival weighted. NTA consumption age profile

9. Golden rule steady states with age structure (2): An Elegant Result • This result is due to Arthur and McNicoll • The effect of a small variation in n on C is found by differentiating across golden rule steady states, and is: • The effect on consumption depends on the balance of the capital dilution effect and an intergenerational transfer effect (actually, all reallocations combined) NTA average ages of consumption and earning.

10. Golden rule steady states with age structure (2): An Elegant Result • This result is due to Arthur and McNicoll • The effect of a small variation in n on C is found by differentiating across golden rule steady states, and is: • The effect on consumption depends on the balance of the capital dilution effect and an intergenerational transfer effect (actually, all reallocations combined) Proportional change in life time consumption when r changes. NTA average ages of consumption and earning.

11. Golden rule steady states with age structure (3): Interpreting this result • Capital dilution will always be negative when n is higher (e.g. with higher fertility). • However, the age structure effect can be positive or negative, depending on the sign of Ac-Ayl • In most Third World countries, I expect that Ac-Ayl <0, with both public and private transfers going mainly to children and the population age distribution young. • In such countries, higher fertility and more rapid population growth is costly, reinforces the capital dilution effect, and leads unambiguously to lower life cycle consumption. • Is Ac-Ayl <0 in the NTA studies we have seen so far? I think so, but I have not seen the average ages calculated.

12. Golden rule steady states with age structure (4): Interpreting for industrial countries • In Industrial countries, Ac-Ayl is probably small or possibly positive because the populations are old, the public sectors transfer heavily to the elderly, and retirement is early. • We need much more evidence from industrial countries. Currently we just have the US and Japan. • I look forward to seeing estimates for France, Sweden, Austria, and Slovenia.

13. Interpretation (cont.) • If reallocations are strongly upward, so that is a large enough number, then the effects of capital dilution can be reversed, and life time consumption can rise even if simple per capita consumption falls.

14. Interpretation (cont.) • After manipulation, the expression can be seen to equal simply T/c, the ratio of transfer wealth to per capita consumption. In other words, the effect of more rapid or less rapid population growth, across golden rule steady states, depends only on the ratio of transfer wealth, in family and public systems, to per capita consumption. This quantity is readily calculated from NTA measures.

15. Golden rule steady states with age structure: Limitations to this approach • Real populations are not stable (steady state) • Real economies are not steady state. • Real economies are not golden rule – generally saving and capital accumulation are lower for various reasons. • There was no theory here about how or why the economy reached the golden rule steady state; I just assumed it. • So now turn to more realistic approaches, and have in mind a changing demographic situation typical of the demographic transition. • Also introduce theory of savings behavior.

16. III. Pure life cycle saving, with no transfers to the elderly (1): Basic idea • Suppose a typical individual has a particular plan for labor supply and earnings over the life cycle, given by yl(x), possibly with a time trend reflecting productivity growth. • This individual (or married couple) wishes to have a smooth consumption path over the life cycle, taking account of: • consumption needs of their children (private transfers to them) • survival probabilities of all members. • Annuities and life insurance enable individuals to budget for the average mortality experience at each age. • Expectations about future productivity growth and interest rates. • Each individual maximizes life time consumption, subject to these constraints and given an intertemporal utility function.

17. Pure life cycle saving, with no transfers to the elderly (2): Demog transition • Original theories: Modigliani, Andy Mason added realistic demography. • Adults accumulate wealth during working years to fund retirement. • After retirement, they dissave. • Demographic transition has several effects: • Lower mortality means longer period in retirement, requires higher saving rate (behavioral) • Lower fertility means adults keep greater share of life time income for own consumption, including in retirement, so need to save more (behavioral) • Older population implies a greater population share of older adults who hold the most wealth (capital), and therefore more capital per person in population (compositional). • Combined effect of demographic transition is to raise capital per worker, thereby raising productivity and income, thereby raising consumption (second dividend effect). • This comes in addition to any first dividend effects (Ac-Ayl)

18. Pure life cycle saving, with no transfers to the elderly (3): Interpretation • In general, there will be less capital than golden rule or than optimal on non-steady state trajectory. • The demog transition will interact with LCS • First, higher saving rates will lead to lower consumption • Later, the greater capital intensity that results will lead to higher consumption. • The demog transition with LCS may move the economy closer to the optimal capital intensity.

19. Pure life cycle saving, with no transfers to the elderly (4): Limitations • LCS theory is controversial • People may not plan as rationally as the theory assumes. • There are complex motives for saving, including precautionary and to make bequests • In reality, there are also intergenerational transfers which must influence rational saving plans • Public education reduces need to provide for own children • Familial old age support and public pensions reduce need to save for old age • If all old age consumption needs were met by transfers, that motive for saving would be removed entirely (but others might appear – e.g. to prepare for costs of supporting elderly parents). • Important to study actual reallocation mechanisms to learn what mix of transfers and savings is used.

20. IV. Mixed Life Cycle Saving, with transfers to the elderly: (1) basic idea • Theory is exactly as for Pure Life Cycle Saving, but now they take as given all public and private patterns of transfers (from NTA estimates!) • what they themselves can expect to receive in the future, and • what they can expect to have to pay in the future in taxes and private transfers • Transfer wealth T is a perfect substitute here for wealth held as Capital, K • Public education reduces future transfers to own children • Transfers to coresident elderly raises need for wealth at time they move in • Transfers expected from own adult children or public pensions reduce need to save for own retirement, etc.

21. Mixed Life Cycle Saving, with transfers to the elderly: (2) Interpretation • Transfer systems can have a down side: they can reduce saving, capital accumulation, and economic growth • Countries should carefully balance these costs of transfer systems against their many benefits when deciding about • Encouraging family support systems • Starting PAYGO public pension systems

22. Mixed Life Cycle Saving, with transfers to the elderly: (3) limitations • Interaction of private optimization behavior with public and private transfer systems is no doubt complex • E.g. Instead of substituting for private capital, a public pension may simply be used by elderly to fund a bequest to their adult children (Barro, Ricardian Equivalence) • Parents may accumulate wealth, and then transfer ownership to their adult children when they move in with them, funding the future transfers they will receive from their children. • Also all the usual concerns about hyper-rationality, complex motives for saving, etc.

23. V. Save so as to maintain transfer wealth as a constant fraction of total pension wealth (fixed τ) • Originally developed by Andy Mason in Mexico City paper • Presented in detail yesterday by Andy, so I won’t repeat. • Appeal is that it is based firmly on the observed realities of public and private transfer systems and actual past saving behavior. • Limitations • Don’t know how τ has changed in the past • Don’t know whether there are systematic sources of change in the future • Note entirely clear what motivation for saving is in this model.

24. VI. Social Planner saving optimally to maximize welfare function depending on level of c(x) profile • Original idea from Cutler, Poterba, Sheiner and Summers (1990) • They assert that optimal saving problem is independent of allocation of total consumption across ages, can solve separately, citing Calvo and Obstfeld. • In Cutler et al, the planner chooses saving and consumption to maximize a social welfare function

25. Social Planner saving optimally to maximize welfare function depending on level of c(x) profile Max discounted time path of consumption per equivalent adult consumer γ

26. Social Planner saving to optimize trajectory of c(x) • Transfers from labor earnings are determined in the model. • It is not clear who owns the capital, so that component of transfers (0 in golden rule) is indeterminate. • I believe this approach will be tractable and yield interesting results on the effects of the demographic transition. • Not yet implemented. • More on this at our January meeting, I hope.

27. Empirical/Simulation Implementations of these approaches • I draw on some older studies and some newer ones to give examples of the results of these theoretical approaches when applied to a population resembling Taiwan’s, 1900 to 2050, but without the immigration in the 1940s. • I will show pure and mixed life cycle saving compared to fixed tau, and look at both savings rates and capital/income ratios.

36. Discussion of these simulations • The most realistic specifications, a priori, are life cycle savings with family transfers, and constant tau=.65. • Comparing these, we note that • under fixed tau, saving rates rise earlier than under LCS, but don’t rise as high. • Same is true for the capital/income ratio • The timing under fixed tau corresponds better to actual savings and capital/income ratios

37. Exploring changing patterns of consumption and labor earnings in the US, 1888-2002 • The US has a striking consumption profile as shown in the next slide. • Consumption rises strongly with age, unlike virtually all other countries where it is flat or falls after the early 20s. • This will have implications for all the kinds of calculations I have discussed before. • How and when did the US get this way?

40. Historical studies for the US • For the US, we have some CEX type surveys of special subpopulations at a few dates • 1888: Industrial workers and their children • 1917: Industrial workers and their children • 1935: Urban Families with Native-Born Head • 1960, 1980, 1990, 2002: US Households • Analyzed (with great care and ingenuity) by Avi Ebenstein and Gretchen Donehouser

41. More on the historical data • Profiles have been adjusted to national control totals • Limitations • These do not include public inkind transfers, only private. • They do not include the flow of services from consumer durables and housing. • Because of varying sample limitations, not strictly comparable. But let’s take a look anyway…

46. Comment on 1888-1960 • Over this 72 year period, consumption has generally been declining with age • At earlier dates, declines following early 20s, like most other NTA countries • By 1960, decline does not start until after 50 or 60 • In the next slide, for 1980, we will see it has become flat across all ages after age 30 or so

48. In 1990, we see that consumption is rising until age 60, and then is flat until 80.

49. This pattern has become even stronger in 2002. Private consumption is about 50% higher in old age than in early 20s.

50. Now let’s look at average ages of private consumption and earnings